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February 2022 On a logarithmic Hardy–Bloch type space, II
Zhihui Zhou, Shanli Ye
Rocky Mountain J. Math. 52(1): 347-363 (February 2022). DOI: 10.1216/rmj.2022.52.347

Abstract

Suppose 0<p and <α<. Let p,α denote the logarithmic Hardy–Bloch type space of those functions f which are analytic in the unit disk 𝔻 such that

fp,α=sup|z|<1(1|z|)(loge1|z|)αMp(|z|,f)<.

In this paper, we mainly obtain the relation between the logarithmic Hardy–Bloch type space p,α and the Hardy space Hp (or the Dirichlet space 𝒟p1p). We also give the characterization of lacunary series on p,α when 1<p.

Citation

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Zhihui Zhou. Shanli Ye. "On a logarithmic Hardy–Bloch type space, II." Rocky Mountain J. Math. 52 (1) 347 - 363, February 2022. https://doi.org/10.1216/rmj.2022.52.347

Information

Received: 28 October 2020; Revised: 28 March 2021; Accepted: 5 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.347

Subjects:
Primary: 30H10 , 30H30

Keywords: Bloch space , Hardy space , lacunary series

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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